ELCT564
Spring 2012
Chapter 5: Impedance Matching
and Tuning
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Impedance Matching
Maximum power is delivered when the load is matched the line and the power loss
in the feed line is minimized
Impedance matching sensitive receiver components improves the signal to noise
ratio of the system
Impedance matching in a power distribution network will reduce amplitude and
phase errors
Complexity
Bandwidth
Implementation
Adjustability
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Matching with Lumped Elements (L Network)
Network for zL inside the 1+jx circle
Network for zL outside the 1+jx circle
Positive X implies an inductor and negative X implies a capacitor
Positive B implies an capacitor and negative B implies a inductor
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Matching with Lumped Elements (L Network)
Smith Chart Solutions
Design an L-section matching network to match a series RF load with an impedance
zL=200-j100Ω, to a 100 Ω line, at a frequency of 500 MHz.
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ZL=2-j1
yL=0.4+j0.5
B=0.29
X=1.22
B=-0.69
X=-1.22
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Matching with Lumped Elements (L Network)
Smith Chart Solutions
B=0.29
X=1.22
B=-0.69
X=-1.22
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Matching with Lumped Elements (L Network)
Smith Chart Solutions
a) An L section LC network is employed for matching a series RC circuit (R=100 Ω,
C=6.366 pF) to a 50 Ω transmission line at 500 MHz. Find the values of L and C.
Show the matching process on the Smith chart and plot the reflection coefficient from
0 to 1 GHz.
C=1.84 pF and L= 19.49 nH
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Single Stub Tunning
Shunt Stub
G=Y0=1/Z0
Series Stub
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Single Shunt Stub Tuner Design Procedure
1. Locate normalized load impedance and draw VSWR circle (normalized load
admittance point is 180o from the normalized impedance point).
2. From the normalized load admittance point, rotate CW (toward generator) on
the VSWR circle until it intersects the r = 1 circle. This rotation distance is the
length d of the terminated section of t-tline. The nomalized admittance at this
point is 1 + jb.
3. Beginning at the stub end (rightmost Smith chart point is the admittance of
a short-circuit, leftmost Smith chart point is the admittance of an open-circuit),
rotate CW (toward generator) until the point at 0 - jb is reached. This rotation
distance is the stub length l.
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Single Stub Tunning
For a load impedance ZL=60-j80Ω, design two single-stub (short circuit) shunt
tunning networks to matching this load to a 50 Ω line. Assuming that the load is
matched at 2GHz and that load consists of a resistor and capacitor in series.
yL=0.3+j0.4
d1=0.176-0.065=0.110λ
d2=0.325-0.065=0.260λ
y1=1+j1.47
y2=1-j1.47
l1=0.095λ
l1=0.405λ
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Single Stub Tunning
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Single Stub Tunning
For a load impedance ZL=25-j50Ω, design two single-stub (short circuit) shunt
tunning networks to matching this load to a 50 Ω line.
yL=0.4+j0.8
d1=0.178-0.115=0.063λ
d2=0.325-0.065=0.260λ
y1=1+j1.67
y2=1-j1.6
l1=0.09λ
l1=0.41λ
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Single Series Stub Tuner Design Procedure
1. Locate normalized load impedance and draw VSWR circle
2. From the normalized load impedance point, rotate CW (toward generator) on
the VSWR circle until it intersects the r = 1 circle. This rotation distance is the
length d of the terminated section of t-tline. The nomalized impedance at this
point is 1 + jx.
3. Beginning at the stub end (leftmost Smith chart point is the impedance of a
short-circuit, rightmost Smith chart point is the impedance of an open-circuit),
rotate CW (toward generator) until the point at 0 ! jx is reached. This rotation
distance is the stub length l.
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Single Stub Tunning
For a load impedance ZL=100+j80Ω, design single series open-circuit stub
tunning networks to matching this load to a 50 Ω line. Assuming that the load is
matched at 2GHz and that load consists of a resistor and inductor in series.
zL=2+j1.6
d1=0.328-0.208=0.120λ
d2=0.5-0.208+0.172=0.463λ
z1=1-j1.33
z2=1+j1.33
l1=0.397λ
l1=0.103λ
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Single Stub Tunning
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Single Stub Tunning
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Double Stub Tunning
The susceptance of the first stub, b1, moves the load
admittance to y1, which lies on the rotated 1+jb circle; the
amount of rotation is de wavelengths toward the load. Then
transforming y1 toward the generator through a length d of
line to get point y2, which is on the 1+jb circle. The second
stub then adds a susceptance b2.
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Double Stub Tunning
Design a double-stub shunt tuner to match a load impedance ZL=60-j80 Ω to a 50 Ω
line. The stubs are to be open-circuited stubs and are spaced λ/8 apart. Assuming
that this load consists of a series resistor and capacitor and that the match frequency
is 2GHz, plot the reflection coefficient magnitude versus frequency from 1 to 3GHz.
yL=0.3+j0.4
b1=1.314
b1 =-0.114
’
y2=1-j3.38
l1=0.46λ
l2=0.204λ
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Double Stub Tunning
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Theory of Small Refelections
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Multisection Transformer
Partial reflection coefficients for a multisection matching transformer
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Binomial Multisection Matching Transformers
The passband response of a binomial matching transformer is optimum in the sense,
and the response is as flat as possible near the design frequency.
Maximally Flat: By setting the first N-1 derivatives of |Г(θ)| to zero at the frequency.
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Binomial Transformer Design
Design a three-section binomial transformer to match a 50Ω load to a 100Ω line, and
calculate the bandwidth for Гm=0.05. Plot the reflection coefficient magnitude versus
normalized frequency for the exact designs using 1,2,3,4, and 5 sections.
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Binomial Transformer Design
Design a three-section binomial transformer to match a 100Ω load to a 50Ω line, and
calculate the bandwidth for Гm=0.05. Plot the reflection coefficient magnitude versus
normalized frequency for the exact designs using 1,2,3,4, and 5 sections.
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Chebyshev Multisection Matching Transformers
Chebyshev transformer optimizes bandwidth
Chebyshev Polynomials
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Design of Chebyshev Transformers
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Design Example of Chebyshev Transformers
Design a three-section Chebyshev transformer to match a 100Ω load to a 50Ω line,
with Гm=0.05, using the above theory.
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Design Example of Chebyshev Transformers
Design a three-section Chebyshev transformer to match a 100Ω load to a 50Ω line,
with Гm=0.05, using the above theory.
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Tapered Lines
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Tapered Lines
Triangular Taper
Klopfenstein Taper
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Tapered Lines
Design a triangular taper, an exponential taper, and a Klopfenstein taper (with
Гm=0.05) to match a 50Ω load to a 100Ω line. Plot the impedance variations and
resulting reflection coefficient magnitudes versus βL.
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